If f(x) and g(x) are integrable functions, th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $F(x) = \int f(x) dx$ and $G(x) = \int g(x) dx$. Then $F'(x) = f(x)$ and $G'(x) = g(x)$.We want to find the expression for $F(x)G(x)$.By the p

Vedclass · Accepted Answer

$\int [f(x) \int g(x) dx + g(x) \int f(x) dx] dx$

Vedclass · Answer

(C) Let $F(x) = \int f(x) dx$ and $G(x) = \int g(x) dx$. Then $F'(x) = f(x)$ and $G'(x) = g(x)$.We want to find the expression for $F(x)G(x)$.By the product rule for differentiation, $\frac{d}{dx}[F(x)G(x)] = F(x)G'(x) + F'(x)G(x) = F(x)g(x) + f(x)G(x)$.Integrating both sides with respect to $x$, we get $F(x)G(x) = \int [f(x)G(x) + g(x)F(x)] dx$.Substituting back $F(x) = \int f(x) dx$ and $G(x) = \int g(x) dx$, we get $F(x)G(x) = \int [f(x) \int g(x) dx + g(x) \int f(x) dx] dx$.

If $f(x)$ and $g(x)$ are integrable functions, then which of the following is equal to $[\int f(x) dx][\int g(x) dx]$?

Similar Questions

$\int x \sec^2 x \, dx = $

If $I(x) = \int x^2(\log x)^2 dx$ and $I(1) = 0$,then $I(x)$ is equal to:

$\int {\left[ {\frac{1}{{\log x}} - \frac{1}{{{{(\log x)}^2}}}} \right]dx = } $

If the primitive of $\cos(\log x)$ is $f(x)\{\cos(g(x)) + \sin(h(x))\}$,then which among the following is true?

If $I = \int \frac{x^2 \, dx}{(x \sin x + \cos x)^2} = f(x) + \tan x + c$, then $f(x)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module